2011 ECAC Playoff Possibilities Time

[Jeff Hopkins '82]

Thanks for the analysis, Robb - I'm more optimstic after that post than I was before it, and the numbers support me.  I feel like I need the extra week off almost as much as the team does.

I hate to rain on the parade, but Robb's analysis seems to treat things as random possibilities.  If we deal with probable outcomes, we can see that it all really comes down to the Princeton-RPI game.

Mind you, I'd rather we took 4 points this weekend, but I'm not holding my breath.

I certainly didn't go to the trouble of calculating the probabilities of each scenario (say, according to KRACH).  Notice that I was careful to say only what percentage of the scenarios were covered by each situation, which is not the same thing as the probability that the situation would occur - unless all of the outcomes are equally likely (i.e. that there's a 1/3 chance that every game ends in a win, tie, or loss).

The only time I mentioned the likeliness of an outcome was that if we "Lose (to Brown), and we'll have less than an 8% shot at a bye unless we can pick up a point at Yale."  I'm fairly confident in that one - Dartmouth surely has more than an 8% chance to pick up 2 points this weekend, which alone would sink our shot at a bye if we lose to Brown.

Robb,

I wasn't criticizing your analysis.  It's actually quite valuable.  And I'm not saying you suggested our real odds are any different because of your analysis.  But if someone interpreted it that way, it would be an unrealistic way to look at things.

[Robb]

Thanks for the analysis, Robb - I'm more optimstic after that post than I was before it, and the numbers support me.  I feel like I need the extra week off almost as much as the team does.

I hate to rain on the parade, but Robb's analysis seems to treat things as random possibilities.  If we deal with probable outcomes, we can see that it all really comes down to the Princeton-RPI game.

Mind you, I'd rather we took 4 points this weekend, but I'm not holding my breath.

I certainly didn't go to the trouble of calculating the probabilities of each scenario (say, according to KRACH).  Notice that I was careful to say only what percentage of the scenarios were covered by each situation, which is not the same thing as the probability that the situation would occur - unless all of the outcomes are equally likely (i.e. that there's a 1/3 chance that every game ends in a win, tie, or loss).

The only time I mentioned the likeliness of an outcome was that if we "Lose (to Brown), and we'll have less than an 8% shot at a bye unless we can pick up a point at Yale."  I'm fairly confident in that one - Dartmouth surely has more than an 8% chance to pick up 2 points this weekend, which alone would sink our shot at a bye if we lose to Brown.

Robb,

I wasn't criticizing your analysis.  It's actually quite valuable.  And I'm not saying you suggested our real odds are any different because of your analysis.  But if someone interpreted it that way, it would be an unrealistic way to look at things.

No worries - I didn't take it that way at all.  Just clarifying!

[Robb]

So....I just happened to have some old code lying around for KRACH and some for figuring out ECAC standings possibilities (who doesn't?), so I linked 'em up, threw a Monte Carlo wrapper around them, and voila!  After a million trials, here are the approximate* probabilities for each team finishing in each place, sorted to the most likely order of finish:

Code Select Expand


1 2 3 4 5 6 7 8 9 10 11 12
Union 81.0% 19.0%
Yale 19.0% 81.0%
Cornell 83.1% 14.7% 2.2%
Dartmouth 9.8% 36.2% 42.7% 11.3%
Rensselaer 2.5% 29.5% 25.3% 42.7%
Princeton 4.6% 19.6% 29.8% 46.0%
Quinnipiac 68.0% 30.6% 1.3% 0.1%
Clarkson 32.0% 68.0%
St. Lawrence 0.8% 54.9% 44.2%
Brown 0.6% 43.8% 45.9% 9.7%
Colgate 9.7% 73.2% 17.0%
Harvard 17.0% 83.0%



It is theoretically possible for Cornell to finish in 6th, but it didn't happen in a single one of the million trials I ran.

*my ECAC tiebreaker code is out of date - I don't have total wins in there as the second tie-breaker, etc, but I'm not going to have time to update it before Friday, so this is the best you get.

[Trotsky]

Thank you, Robb.  That is terrific.

[billhoward]

And people think there is no real world use of math beyond calculating 18% of the check. The breakout makes it a lot clearer that Cornell with a weekend split is in pretty good shape. Thank you!

[Jim Hyla]

You certainly are a lot more productive at 5:30 AM, when I posted my Playoff Poll, than I am.:-D

[Jeff Hopkins '82]

Wow.  Just wow.

[Robb]

You certainly are a lot more productive at 5:30 AM, when I posted my Playoff Poll, than I am.:-D

11h30 ici a Geneve...

[Jim Hyla]

You certainly are a lot more productive at 5:30 AM, when I posted my Playoff Poll, than I am.:-D

11h30 ici a Geneve...

So, I see now.::doh::

[Rita]

So....I just happened to have some old code lying around for KRACH and some for figuring out ECAC standings possibilities (who doesn't?), so I linked 'em up, threw a Monte Carlo wrapper around them, and voila!  After a million trials, here are the approximate* probabilities for each team finishing in each place, sorted to the most likely order of finish:

Code Select Expand


1 2 3 4 5 6 7 8 9 10 11 12
Union 81.0% 19.0%
Yale 19.0% 81.0%
Cornell 83.1% 14.7% 2.2%
Dartmouth 9.8% 36.2% 42.7% 11.3%
Rensselaer 2.5% 29.5% 25.3% 42.7%
Princeton 4.6% 19.6% 29.8% 46.0%
Quinnipiac 68.0% 30.6% 1.3% 0.1%
Clarkson 32.0% 68.0%
St. Lawrence 0.8% 54.9% 44.2%
Brown 0.6% 43.8% 45.9% 9.7%
Colgate 9.7% 73.2% 17.0%
Harvard 17.0% 83.0%



It is theoretically possible for Cornell to finish in 6th, but it didn't happen in a single one of the million trials I ran.

*my ECAC tiebreaker code is out of date - I don't have total wins in there as the second tie-breaker, etc, but I'm not going to have time to update it before Friday, so this is the best you get.

Thanks Robb! Now I can tell my family there is a 97.8% chance they will see me next weekend . Life is so much more predictable when hockey games are played inside computers. :-P

[Robb]

Life is so much more predictable when hockey games are played inside computers. :-P

Unfortunately, they all are for me...  I haven't even managed to go see the local Swiss league team this year.  

[Trotsky]

Life is so much more predictable when hockey games are played inside computers. :-P

Unfortunately, they all are for me...  I haven't even managed to go see the local Swiss league team this year.  

Me too.  Reason #483 why they need to get to Atlantic City.  I have a 29-year streak of seeing at least one game on the line.

[Beeeej]

So....I just happened to have some old code lying around for KRACH and some for figuring out ECAC standings possibilities (who doesn't?), so I linked 'em up, threw a Monte Carlo wrapper around them, and voila!  After a million trials, here are the approximate* probabilities for each team finishing in each place, sorted to the most likely order of finish:

Code Select Expand


1 2 3 4 5 6 7 8 9 10 11 12
Union 81.0% 19.0%
Yale 19.0% 81.0%
Cornell 83.1% 14.7% 2.2%
Dartmouth 9.8% 36.2% 42.7% 11.3%
Rensselaer 2.5% 29.5% 25.3% 42.7%
Princeton 4.6% 19.6% 29.8% 46.0%
Quinnipiac 68.0% 30.6% 1.3% 0.1%
Clarkson 32.0% 68.0%
St. Lawrence 0.8% 54.9% 44.2%
Brown 0.6% 43.8% 45.9% 9.7%
Colgate 9.7% 73.2% 17.0%
Harvard 17.0% 83.0%



It is theoretically possible for Cornell to finish in 6th, but it didn't happen in a single one of the million trials I ran.

*my ECAC tiebreaker code is out of date - I don't have total wins in there as the second tie-breaker, etc, but I'm not going to have time to update it before Friday, so this is the best you get.

Fanfreakin'tastic.

[jtwcornell91]

So....I just happened to have some old code lying around for KRACH and some for figuring out ECAC standings possibilities (who doesn't?), so I linked 'em up, threw a Monte Carlo wrapper around them, and voila!

What probability did you assign to a tie in any given game?

[jtwcornell91]

Life is so much more predictable when hockey games are played inside computers. :-P

Unfortunately, they all are for me...  I haven't even managed to go see the local Swiss league team this year.  

Tant pis.  Presumably you would have had more incentive when Knoepfli (sorry, Knöpfli) was still playing for Genève-Servette.